With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phen...With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.展开更多
Some new structures and interactions of solitons for the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable separation approach. The soluti...Some new structures and interactions of solitons for the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable separation approach. The solutions to describe the interactions between two dromions, between a line soliton and a y-periodic soliton, and between two y-periodic solitons are included in our results. Detailed behaviors of interaction are illustrated both analytically and in graphically. Our analysis shows that the interaction properties between two solitons are related to the form of interaction constant. The form of interaction constant and the dispersion relationship are related to the form of the seed solution （u0, v0, w0 ） in Backlund transformation.展开更多
The interaction of three conormal waves for semi-linear strictly hyperbolic equations of third order is considered. Let Σi, i = 1, 2, 3, be smooth characteristic surfaces for P= Da(D_t￣2 -△) intersecting transversa...The interaction of three conormal waves for semi-linear strictly hyperbolic equations of third order is considered. Let Σi, i = 1, 2, 3, be smooth characteristic surfaces for P= Da(D_t￣2 -△) intersecting transversally at the origin. Suppose that the solution u to Pu = f(t, x ,y)D u), ≤2 is conormal to Σi, i = 1, 2, 3, for t < 0. The author uses Bony's second microlocajization techniques and commutator arguments to conclude that the new singularities a short time after the triple interaction lie on the surface of the light cone Γ over the origin plus the surfaces obtained by flow-outs of the lines of intersection Γ ∩ Σi and Σi∩ Σj, i, j = 1, 2, 3.展开更多
文摘With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.
基金The project supported by the State Key Laboratory of 0il/Gas Reservoir Geology and Exploitation ＂PLN0402＂The authors would like to thank Prof.Sen-Yue Lou for helpful discussions.
文摘Some new structures and interactions of solitons for the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable separation approach. The solutions to describe the interactions between two dromions, between a line soliton and a y-periodic soliton, and between two y-periodic solitons are included in our results. Detailed behaviors of interaction are illustrated both analytically and in graphically. Our analysis shows that the interaction properties between two solitons are related to the form of interaction constant. The form of interaction constant and the dispersion relationship are related to the form of the seed solution （u0, v0, w0 ） in Backlund transformation.
文摘The interaction of three conormal waves for semi-linear strictly hyperbolic equations of third order is considered. Let Σi, i = 1, 2, 3, be smooth characteristic surfaces for P= Da(D_t￣2 -△) intersecting transversally at the origin. Suppose that the solution u to Pu = f(t, x ,y)D u), ≤2 is conormal to Σi, i = 1, 2, 3, for t < 0. The author uses Bony's second microlocajization techniques and commutator arguments to conclude that the new singularities a short time after the triple interaction lie on the surface of the light cone Γ over the origin plus the surfaces obtained by flow-outs of the lines of intersection Γ ∩ Σi and Σi∩ Σj, i, j = 1, 2, 3.
